1. Unit Inputs, Systems, and System Properties
August 30, 2000 EE 64, Section 1 ©Michael R. Gustafson II Pratt School of Engineering

2. Last Time Definition of a signal Signal energy and power
Even and odd signals
Even and odd parts of a signal

3. Important Discrete Signals
Discrete unit impulse:
Discrete unit step:

4. Discrete Signal Relationships
The unit step can be written as a function of the unit impulse: The unit impulse can be written as a function of the unit step:

5. Important Continuous Signals
Continuous unit impulse:
Continuous unit step: ( ) î í ì
>
< = , 1 t u

6. Continuous Signal Relationships
The unit step can be written as a function of the unit impulse: The unit impulse can be written as a function of the unit step: ( ) t u dt d =

7. Systems What is a system?
"Physical systems in the broadest sense are an interconnection of components, devices, or subsystems"
For this class, we will mostly be dealing with the relationship between the inputs to a system and the outputs from a system.

8. System Properties
There are several system properties that describe how the inputs and outputs interact:
Linearity
Time Invariance
Memory
Causality
Stability
Invertibility

9. Linearity
A system S is linear if it follows three basic rules:

10. Time Invariance
A system S is time invariant if it follows one basic rule:

11. Other "Timing" Properties
Memoryless: a system S is memoryless if the output is dependent solely on the input at the present time.
Causal: a system S is causal if the output is dependent on the input at the present time or in the past but not in the future.
Can a physical system be non-causal?

12. Stability
A system S is stable if, for any bounded input, there is a bounded output.
Usually in this class, you will seek to disprove stability by example rather than to prove stability through rigorous arithmetic.

13. Invertibility
A system S is invertible if a distinct set of inputs leads to a distinct set of outputs.
Invertibility is not critical to this class -- but is very important for communications systems, especially encrypted ones.

14. Examples

15. Assignment Read Chapter 1 and skim Chapter 2 of OW.
Start the homework assignment.
The TA's will be available as listed in the sent out last night

16. Next Time
Block diagram introduction
Review of Chapter 1

17. Questions ?